# Technical Studies Reference

### Inverse Fisher Transform with RSI

The study calculates and displays an Inverse Fisher Transform of an RSI.

Let $$C$$ be a random variable denoting the Close Price, and let the RSI Length and RSI MovAvg Length Inputs be denoted as $$n_{RSI}$$ and $$n_{\overline{RSI}}$$, respectively. The Moving Average used in computing $$RSI_t(C,n_{RSI})$$ is determined by the RSI Internal MovAvg Type Input. We subject the RSI to the following transformation.

$$RSI^*_t(C,n_{RSI}) = \frac{1}{10}\left(RSI_t(C,n_{RSI}) - 50\right)$$

We denote the Weighted Moving Average of $$RSI^*_t(C,n_{RSI})$$ as $$\overline{RSI^*}_t(C,n_{RSI},n_{\overline{RSI}})$$, and we compute it as follows.

$$\overline{RSI^*}_t(C,n_{RSI},n_{\overline{RSI}}) = WMA_t\left(RSI^*(C,n_{RSI}), n_{\overline{RSI}}\right)$$

The Inverse Fisher Transform with RSI is at Index $$t$$ is then given by $$IFT_t\left(\overline{RSI^*}(C,n_{RSI},n_{\overline{RSI}})\right)$$. The explicit formula is given below. It is calculated for $$t \geq n_{RSI} + n_{\overline{RSI}}$$.

$$\displaystyle{IFT_t\left(\overline{RSI^*}(C,n_{RSI},n_{\overline{RSI}})\right) = \frac{\exp\left(2\overline{RSI^*}(C,n_{RSI},n_{\overline{RSI}})\right) - 1}{\exp\left(2\overline{RSI^*}(C,n_{RSI},n_{\overline{RSI}})\right) + 1}}$$

Let the Line Value Input be denoted as $$l$$. In addition to the graph of $$IFT_t\left(\overline{RSI^*}(C,n_{RSI},n_{\overline{RSI}})\right)$$, this study displays horizontal lines at levels $$\pm l$$.